Answer:
x ≈ 77.5°
Step-by-step explanation:
Using the tangent ration in ΔBCD
tan38° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DC}{DB}[/tex] = [tex]\frac{DC}{3.5}[/tex]
Multiply both sides by 3.5, then
DC = 3.5 × tan38° ≈ 2.734
Using the sine ratio in ΔACD
sinx° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{DC}{AC}[/tex] = [tex]\frac{2.734}{2.8}[/tex]
x = [tex]sin^{-1}[/tex]( [tex]\frac{2.734}{2.8}[/tex] ) ≈ 77.5°
